The Scot has plotted the run-ins of the two north-west rivals and believes the Anfield side will come out on top by a single point.
With eight games of a neck-and-neck battle to play, Liverpool currently trail Pep Guardiola's men by a point after both sides secured home wins over the weekend.
Jurgen Klopp's side held a seven-point lead at the turn of the year but City slowly whittled away at that advantage before returning to the summit at the start of this month.
However, McAllister, 54, who played for the club between 2000 and 2002, says Liverpool can turn the tables on their rivals and end a title drought that stretches back to 1990.
The former Scottish international told Sky Sports: "I've looked at both run-ins and done a predictor and I thought I would favour Manchester City.
"But the way it's turned out I still have Liverpool coming out on top by a point."
Liverpool have not won the title during the Premier League era - but McAllister says they must block out the pressure that goes with that unwanted record to have a chance of beating City to the crown.
"There is immense pressure and the players will be well aware of it - even though they will say they are not taking it into consideration," added McAllister.
"There is a lot of outside noise around the fact Liverpool haven't won for such a long time.
"But they've just got to try to focus on each and every game and take each one in isolation."
Liverpool travel to Germany to take on Bayern Munich in a Champions League last-16 second leg tie poised at 0-0 on Wednesday, before a trip to play Fulham at Craven Cottage in the Premier League on Sunday afternoon.
City are also in Champions League action against a German side in the form of Schalke, holding a 3-2 lead going into Tuesday night's second leg at Etihad Stadium.
Guardiola's side will then turn their attention to the FA Cup and a quarter-final tie against Championship side Swansea at the Liberty Stadium on Saturday.